Bababa ba?

Invalid argument

If I do not study in Stat117 then I will fail the course.
I studied in Stat 117.
Therefore, I will not fail the course.

—

Let p: I studied in Stat 117
q: I will fail the course

The above argument states that

~p → q
p
therefore: ~q

But, as the title of this entry says, it is an invalid argument. There are no Rules of Inference that state that the conjunction (~p => q) and p will leave us with ~q. Thus, even if I studied, I cannot logically conclude/predict that I will pass the course.

The following truth table further disproves the above argument

But, if I did not study, the second premise would be modified, and so

~p → q
~p
therefore: q (by Modus Ponens).

So yeah. Because Modus Ponens says so, I will fail the course. :p

And I computed that the chances of me perfecting a set of 5 multiple choice questions, with 4 choices each, just by guessing is 1 out of 4×4x4×4x4 or 1 out of 1024. So what more if the exam is composed 50 multiple choice items?